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Seismic Analysis/Design of Multi-storied RC Buildings
using STAAD.Pro & ETABSaccording to IS:1893-2002
Presented by . Rahul Leslie
Assistant Director,Buildings Design,
DRIQ, Kerala PWDTrivandrum, India
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Topics Covered:
• Computer modelling and analysis using STAAD.Pro & ETABS for– Seismic Coefficient method as per IS:1893
(Part 1)-2002
– Response Spectrum method as per IS:1893(Part 1)-2002
• Miscellaneous points
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Aspects of Computer Model:• Modelling is done using analysis packages like
STAAD.Pro, STRAP, NISA Des. Studio, ETABS, GT STRUDL, RISA-3D, MIDAS-Gen, etc.
• Model contains • Beams• Columns• Shear walls
But not usually• Slabs (except in Flat slab - Shear wall construction)
• Masonry wall infills• Stair slabs
Foundation is represented by support points only
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Model for ETABS: B+G+4=6 stories
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS Model
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS Model
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Model for STAAD: G+4 = 5 stories
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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STAAD Model
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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STAAD Model
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Aspects of Computer Model (Cont…)• A model must ideally represent the complete three
dimensional (3D) characteristics of the building, including – geometry– stiffness of various members– supports– load distribution– mass distribution
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Beams and columns• Beams and columns are modelled by frame elements• Plinth beams should also be modelled as beams• Slabs are not usually modelled
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Supports:• The type of support to be provided is decided by
considering the degree of fixity provided by the foundation.
• Fixed Supports:– Raft foundation: Support to be provided at the column
ends (located at top of the raft)– Pile cap for multiple piles: Support to be provided at the
column ends (located at top of the pile cap)– Isolated footing: When it is founded on hard rock, the
column end may be modelled as fixed (located at the top of the footing)
– Single pile: Fixed support of the column is recommended at a depth of five to ten times the diameter of pile, depending upon the type of soil, from the top of pile cap.
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Supports (cont…):• Pinned supports:
– Isolated footing: Support to be provided at the column ends, (located at the bottom of the foundation).
• Spring supports: – Spring supports can be provided with spring constants ,
eg., as per ASCE/SEI 41(2006)
• In General– Engineering judgement must be exercised in modelling the
support
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Slabs and Masonry walls• The weight of slabs are distributed, as 2-way load, on
the supporting beams. • The weight of masonry walls are applied as uniform
load on the supporting beam
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Slabs and Masonry walls• Since the slabs are not modelled by plate elements, the
structural effect due to their in-plane stiffness (7.7.2.1, IS:1893(Part 1)-2002) can be taken into account by – using ‘Master/Slave’ option (STAAD.Pro)– assigning ‘Diaphragm’ action (ETABS , STAAD.Pro V8i
Sel.4)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Assign diaphragms: select all slabs in a storey and …
ETABS: Floor Diaphragm
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS: Floor Diaphragm
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS: Floor Diaphragm
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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STAAD: Floor Diaphragm
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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STAAD: Floor Diaphragm
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Shear walls• Structural shear walls and Shear core which are
integrally connected to the frame and floor slabs, can be modelled by plate elements – ‘Surface elements’ (STAAD.Pro)
– ‘Wall element’ (ETABS)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Analysis as per IS:1893-2002
Seismic Coefficient Method (Static Analysis)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis:
• The Design horizontal seismic coefficient Ah is calculated from (6.4.2, IS:1893(Part 1)-2002)
– Zone factor Z (Table 2, IS:1893(Part 1)-2002)– Importance factor I (Table 6, IS:1893(Part 1)-2002)– Response reduction coefficient R (Table 7, IS:1893(Part 1)-2002)
– Horizontal Acceleration coefficient Sa/g
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis:• Where the Horizontal acceleration Sa/g is determined
from the Response spectrum curve (Fig.2, IS:1893(Part 1)-2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis (cont…):
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis (cont…):
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis:• The time period of the structure is determined using
(7.6.1 & 7.6.2, IS:1893(Part 1)-2002)– RC frames without brick infills
h = height of building in m– RC frames with brick infills
d = base dimension in m(parallel to direction of earthquake)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Static analysis (cont…):• Where the type of soils are
– Type I (Rock or Hard soil): N > 30, among other descriptions– Type II (Medium soils): 10 ≤ N ≤ 30 for all soils
N >15 for poorly graded, among other descriptions
– Type III (Soft soils): N < 10(Table 1, IS:1893(Part 1)-2002)
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Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
Cl.6.4.4, IS:1893(Part 1)-2002
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Static analysis:• Importance factor (Table 6, IS:1893(Part 1)-2002)
– I = 1.5 for special buildings– I = 1.0 for other buildings
• Response reduction factor (Table 7, IS:1893(Part 1)-2002)– R = 3 for ordinary detailing (with ordinary detailed shear
wall, if any)– R = 5 for ductile detailing (with ductile detailed shear wall, if
any) ie., as per IS:13920-1993– R = 4 for ductile detailing with ordinary detailed shear wall– R = 4.5 for ordinary detailing with ductile detailed shear wall
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Static analysis (cont…):• The base shear is determined by (7.5.3, IS:1893(Part 1)-
2002)
• Design lateral force for each level is determined by (7.7.1, IS:1893(Part 1)-2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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A Simple Example
A six storied structure
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Lumped mass model
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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height 18 m
Period 0.075x(18)0.75 = 0.6554 sec
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
(Assumed to be open structure)
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Levels W (kN) h (m) Wh2
ΣW*(Wh2/ΣWh2) Qi (kN)
1 0 0 0 0 0
2 23.57 3 212.13 1.5541 0.0632
3 23.57 6 848.52 6.2163 0.2529
4 23.57 9 1909.17 13.9866 0.5691
5 23.57 12 3394.08 24.8651 1.0117
6 23.57 15 5303.25 38.8516 1.5807
7 23.57 18 7636.68 55.9464 2.2763
ΣW 141.42 (kN) 19303.83 141.42 kN 5.7539 kN
Vb 5.7539 (kN)
height 18 m
Period 0.6554 sec
Sa/g 1.5258
Ah 0.0407
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
= (ZI)/(2R) x sa/g= (0.16*1)/(2*3) * 1.5258
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The forces are applied …and analysed
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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The forces are applied
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Seismic Coeff. method
ETABS: Define & Apply Seismic
parameters:• Direction• T
• Z, I, R
• Soil Type
STAAD: Define Seismic parameters:
• Z, I, R• Structure Type or
Tx & Tz
• Soil Type • Damping ratio ξ
Apply
• Direction (X, Y,Z), factor
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
41ETABS: Seismic coeff. method
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
42STAAD: Seismic coeff. method
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
43STAAD: Seismic coeff. method
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Masses to be included:• For seismic analysis, the effective masses to be
included for analysis are :– Full dead load– 0.25 times Imposed Loads having intensity ≤ 3 kN/m2
– 0.5 times Imposed Loads having intensity > 3 kN/m2
– Imposed Load on roof need not be considered(7.3.1,7.3.2 & Table 8, IS:1893(Part 1)-2002)
• Live load reduction for upper floors (as per 3.2, IS:875(Part 2) - 1987) shall not be applied further for mass calculation (7.3.3, IS:1893(Part 1) - 2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Add Seismic Masses
EATBS• Select loads to
combine
STAAD• Add self wt., Joint
loads, Member loads, Floor loads
OR• Put lumped mass
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Define Mass Source:-
ETABS: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
47STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
48STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
49STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
50STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
51STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
52STAAD: Seismic masses
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
STAAD.Pro V8i SELECT 4
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Results of Seismic Analysis – Bending Moment & Shear Force
• Gravity Loads – Bending Moment
• Gravity Loads – Shear Force
• Seismic Loads – Bending Moment
• Seismic Loads – Shear Force
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
55Load combinations: will be covered later
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS: Run Analysis
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
57ETABS: Gravity Loads Bending Moment
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
58ETABS: Gravity Loads Shear Force
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
59ETABS: Seismic Force in Z direction Bending Moment
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
60ETABS: Seismic Force in Z direction Shear Force
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
61STAAD: Run Analysis
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
62STAAD: Gravity Loads Bending Moment
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
63STAAD: Gravity Loads Shear Force
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
64STAAD: Seismic force in Z direction Bending Moment
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
65STAAD: Seismic force in Z direction Shear Force
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Analysis as per IS:1893-2002
Response Spectrum Method (Dynamic Analysis)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Response spectrum analysis:• Response spectrum analysis is performed using multi-
mode responses, where the free vibration modes are computed using – Eigen vector analysis (STAAD.Pro)– Eigen vector or Ritz Vector analysis (ETABS)
• The modal parameters for a structure come as pairs of – Natural Frequency f (in Hz) – Mode shape φ
• The modal parameters for few of the lower frequencies are considered for further calculations (7.8.4.2, IS:1893(Part 1)-2002), based on the following;– Modes for frequencies > 33 Hz need not be considered– The no. of modes considered should be such that the total
mass participation factor should be at least 90%– Missing mass correction for modes beyond 33Hz
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Response spectrum analysis (cont…):• For the modal parameters considered, the following
factors are determined for each mode– Mode participation factor of each mode Pk
– Mass participation factor for each mode Mk – Spectral Acceleration coefficient (Sa/g)
• The Design horizontal seismic coefficient Ah is calculated for each mode from (6.4.2, IS:1893(Part 1)-2002)
– Zone factor Z – Importance factor I– Response reduction coefficient R– Spectral Acceleration coefficient Sa/g
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Response spectrum analysis (cont…):• Where the Horizontal acceleration Sa/g is determined
from the Response spectrum curve (Fig.2, IS:1893(Part 1)-2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Response spectrum analysis (cont…):• The lateral force due to the modal response
(considering the mode participation factor) is obtained for each mode of all the modes considered. The the force at each level for each mode is calculated as (7.8.4.5 (c), IS:1893(Part 1)-2002):
Where– Ak is the design horizontal seismic coefficient
– φik is the mode shape value for that floor level– Pk is mode participation factor– Wi is mass at that floor level
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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The Same Simple Example
A six storied structure
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Lumped mass model
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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MODAL ANALSYSEIGEN VALUES
EIGEN VECTORS
Mode Shapes
Natural Frequencies
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Different types of modes: 1.Translational mode in X direction
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Different types of modes: 2.Translational mode in Y direction
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Different types of modes: 3.Torsional mode
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Mode 1
Freq. = 1.44119 Hz
Period = 0.69387 sec Mode shape = 0
0.15130.36870.57960.76310.90591
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Mode 2
Freq. = 4.51039 Hz
Period = 0.22171 sec Mode shape = 0
-0.5293-1-0.9604-0.41100.366290.98395
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Modes I II III IV V
Levels Mode Shapes
1 0 0 0 0 0
2 0.151 -0.53 0.824 -1 1
3 0.369 -1 0.861 -0.047 -0.836
4 0.58 -0.96 -0.24 0.999 0.027
5 0.763 -0.41 -1 -0.265 0.813
6 0.906 0.366 -0.38 -0.902 -0.989
7 1 0.984 0.804 0.606 0.415
Period (sec) 0.694 0.222 0.123 0.085 0.065
Freq(Hz) 1.441 4.51 8.098 11.78 15.31
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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For kth mode,
Where, n = no. of levels
m = no. of modes
Mode I II III IV V
Mk(kN) 115.5 16.31 5.424 2.686 1.237
Participating mass =115.5+16.31+5.424+2.686+1.237=141.183kN
Total mass = 23.57 x 6 = 141.42 kN
Mass participation = 100x141.183/141.42 = 99.8326% > 90% .:Okay
Check Mass Participation (7.8.4.5(a), IS:1893(Part 1)-2002)
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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For kth mode,
Where, n = no. of levels
Mode I II III IV V
Pk 1.30049 -0.44635 0.26529 -0.18718 0.12223
Calculate Mode Participation factors (7.8.4.5(b), IS:1893(Part 1)-2002)
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
8282
x 1.30049
x 0.26529
x -0.44635
x -0.18718
x 0.12223+
++
+
Calculate Mode Participation factors
=
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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=
(Had all the mode shapes been utilized)
Calculate Mode Participation factors
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Modes I II III IV V
Φ’s
1 0 0 0 0 0
2 0.1513 -0.5293 0.8237 -1 1
3 0.3688 -1 0.8614 -0.0466 -0.8364
4 0.5796 -0.9604 -0.239 0.999 0.0268
5 0.7631 -0.4111 -1 -0.2653 0.8128
6 0.906 0.3663 -0.382 -0.9023 -0.9892
7 1 0.984 0.8038 0.6064 0.4154
W
0
23.57
23.57
23.57
23.57
23.57
23.57
WΦ
0 0 0 0 0
3.566 -12.48 19.415 -23.57 23.57
8.692 -23.57 20.303 -1.097 -19.71
13.66 -22.64 -5.6354 23.547 0.631
17.99 -9.689 -23.57 -6.253 19.16
21.35 8.6335 -9.0113 -21.27 -23.32
23.57 23.192 18.946 14.292 9.791
88.83 -36.55 20.447 -14.35 10.12
WΦ2
0 0 0 0 0
0.54 6.6043 15.992 23.57 23.57
3.206 23.57 17.488 0.0511 16.49
7.919 21.74 1.3474 23.524 0.017
13.73 3.9826 23.57 1.659 15.57
19.34 3.1623 3.4452 19.19 23.07
23.57 22.819 15.228 8.6658 4.067
68.3 81.879 77.072 76.66 82.78
Mk 115.5 16.313 5.4243 2.6859 1.2369
Pk 1.300 -0.4464 0.2653 -0.1872 0.1222
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Period 0.693 0.221 0.123 0.084 0.065
Sa/g 1.4411 2.5 2.5 1.1273 1.0979
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Calculate Design horizontal seismic coefficient
Z = Zone factor = 0.16 I = Importance factor = 1R = Response reduction coefficient = 3
Period 0.693 0.221 0.123 0.084 0.065
Sa/g 1.441 2.5 2.5 1.1273 1.0979
Ah 0.0384 0.0667 0.0667 0.0300 0.0292
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Calculate horizontal force due to each mode
0.0384 x 1.30049 x
0
0.151
0.369
0.58
0.763
0.906
1
=
0
0.178
0.434
0.683
0.899
1.067
1.178
Eg: - for mode 1 :
kN
0
23.57
23.57
23.57
23.57
23.57
23.57
*
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Combining Modes:(a) Indirect method
(Supported by all codes –
IS, BS, EC, etc.)
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Mode I II III IV V
Levels Qik (kN)
1 0 0 0 0 0
2 0.178 0.371 0.343 0.133 0.084
3 0.434 0.701 0.359 0.006 -0.071
4 0.683 0.674 -0.1 -0.133 0.002
5 0.899 0.288 -0.42 0.035 0.069
6 1.067 -0.26 -0.16 0.12 -0.083
7 1.178 -0.69 0.335 -0.08 0.035
Calculate horizontal force due to each mode…
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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From each mode characteristics…
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Calculate horizontal force due to each mode… apply and…
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
Analyse for forces, and combine the forces to get final forces…
9393
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
Analyse for forces, and combine the forces to get final forces…
9494
Combining Modes:(a) Direct method
(Supported by FEMA 356, etc.
for Non-linear Static Analysis*)
*Pushover Analysis
9595
Mode I II III IV V
Levels Qik (kN)
1 0 0 0 0 0
2 0.178 0.371 0.343 0.133 0.084
3 0.434 0.701 0.359 0.006 -0.071
4 0.683 0.674 -0.1 -0.133 0.002
5 0.899 0.288 -0.42 0.035 0.069
6 1.067 -0.26 -0.16 0.12 -0.083
7 1.178 -0.69 0.335 -0.08 0.035
Calculate horizontal force due to each mode… and combined
SRSS
0
0.559
0.903
0.973
1.035
1.119
1.409
Eg: - for level 7:
SRSS = √[(1.178)2 + (-0.69)2 + (0.335)2 + (-0.08)2 + (0.035)2] = 1.409
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Calculate horizontal force due to each mode… and combined
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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The forces are applied… …and analysed
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Indirect method Direct method
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
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Combination of modal responses with…
(1) Dominant mode:• When activated, all modal combination results will
have the same sign as the dominant mode shape alone would have if it were excited and then the scaled results were used as a static displacements result.
(2) Signed value:• This option results in the creation of signed values for
all results. The sum of squares of positive values from the modes are compared to sum of squares of negative values from the modes. If the negative values are larger, the result is given a negative sign.
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
STAAD.Pro V8i SELECT 4
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Methods of mode combinations
IS:1893 and other sources
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I II III IV V VI VII VIII
1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 … (Hz)
93.223 %
99.922 % 0.077 %
Out-of-phase modesOR
Periodic Response
In-phase modesOR
Rigid Response
33 Hz
ZPA
Modal Combination(ABS, SRSS,CQC, etc.)
Missing Mass Correction
Combination of Periodic and Rigid modes
(Lindley-Yow, Hadjian, etc. )
Mode frequencies – an overview:
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Combination of modal responses:
1. Absolute Combination (ABS)– The modal responses of all the individual modes are
summed up (to be used in modal combination as per IS:1893-1984) :
– Eg. for level 7,ABS = │1.178│ + │-0.69│ + │0.335│ + │-0.08│ + │0.035│ = 2.318
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Combination of modal responses (cont…):
2. Square Root of Sum of Squares (SRSS)– The modal responses are squared, summed, and the root of
the sum taken:
– Eg. for level 7,SRSS = √[(1.178)2 + (-0.69)2 + (0.335)2 + (-0.08)2 + (0.035)2] = 1.409
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Combination of modal responses (cont…):
3. Combination of ABS and SRSS (ABS&SRSS)– The weighted sum of ABS and SRSS is taken– The method was prescribed in IS:1893-1984 (4.2.2.2, IS:1893-
1984), removed in IS:1893(Part 1)-2002
– Values for γ are given by table – Intermediate values can be
obtained by interpolation Note: γ1 + γ2 = 1
– Eg. for level 7,
ABS&SRSS = 0.6 x 2.318 + 0.4 x 1.408 = 1.954
H (m) γ1 γ2
20 0.6 0.4
40 0.4 0.6
60 0.2 0.8
90 0.0 1.0
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Combination of modal responses (cont…):
4. Out-of-phase response combination– This is a general category of methods, which includes CQC
and SRSS– The general equation is
where ρij is the cross modal coefficient
a) SRSS method• SRSS can be represented as ρij = 1 for i=j = 0 for i≠j
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Combination of modal responses (cont…):
5. Out-of-phase response combination (cont..)b) Complete Quadratic Combination (CQC)
• The CQC equation prescribed by IS:1893-2002 is (7.8.4.4, IS:1893(Part 1)-2002)
where ζ is the damping ratio ( 0.05 for RCC)and β = ωj/ωi
( )Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Response spectrum method
ETABS Define Seismic
parameters:• Zone • Soil Type
Apply Seismic parameters
• Damping ratio ξ• Method of comb (SRSS,
CQC, etc.)• Method of Dir. Comb• Direction (X, Y, Z)• I, R
STAAD Define& apply Seismic
parameters:• Damping ratio ξ• Method of comb (SRSS,
CQC, etc.)• Soil Type• Direction (X, Y, Z)• Scale (= Z.I / 2.R)• Normalization Scale (= 9.8)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
108ETABS: Define Response SpectrumSeismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Scale factor = gI/(2R) = 9.81*1/(2*5) = 0.981
ETABS: Apply Response Spectrum
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110110
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111111
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
112112STAAD: Response SpectrumSeismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
ZI / 2R = 0.024
113113STAAD: Response Spectrum
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STAAD.Pro V8i SELECT 4
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115115
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Directional Combination of Modal Responses
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Directional combination of modal responses:
• As per IS:1893, directional combination need to be done only when the lateral load resisting members are not oriented along horizontal orthogonal directions (6.3.2.2, IS:1893(Part 1)-2002)
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Directional combination of modal responses:1. SRSS Method (6.3.4.2, IS:1893(Part 1)-2002)
– The method combines the directional components by SRSS method. The method is prescribed in IS:1893-2002 as an alternative to SAS method
2. Scaled Absolute Sum method (SAS)– The method combines the directional components by sum
of values in one direction, with 0.3 times the sum of values in the other directions (6.3.4.1, IS:1893(Part 1)-2002)
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No. of Modes & Missing mass correction
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I II III IV V VI VII VIII
1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 … (Hz)
93.223 %
99.922 % 0.077 %
Out-of-phase modesOR
Periodic Response
In-phase modesOR
Rigid Response
33 Hz
ZPA
Modal Combination(ABS, SRSS,CQC, etc.)
Missing Mass Correction
Mode frequencies – an overview:
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Missing Mass Correction :
• Missing Mass = 0.077% of total mass• Zero Period Acceleration (3.11, IS:1893(Part 1)-2002) = 1.6
I II III IV V VI VII VIII
1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 … (Hz)
99.922 % 0.077 %
33 Hz
ZPA
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Missing Mass Correction :
• Missing Mass = 0.077% of total mass• Zero Period Acceleration, (Sa/g)ZPA = 1.6 (3.11, IS:1893(Part 1)-
2002) • Horizontal acceleration coefficient, Ah
I II III IV V VI VII VIII
1.441 4.51 8.098 11.782 15.309 17.908 69.357 103.083 … (Hz)
99.922 % 0.077 %
33 Hz
ZPA
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Missing Mass Correction (cont…):
• Lateral force, QR is given by
where Mmiss.mass is the missing mass
Mk(ZPA) is sum of Participating masses up to ZPA
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Storey wise Mass Participation for 1st mode
0
4.6285
11.310
17.778
23.387
27.771
30.652
=
For 1st mode, Mk = 0+4.6285+11.310+17.778+23.387+27.771+30.652 = 115.52
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
Thus, storey wise Mass Participation can be obtained for each mode, from which the total storey wise Mass Participation,
and consequently, the storey wise Missing Mass can be determined.
125
Storey wise Missing mass
(kN)
0
0.0155
0.0243
0.0256
0.0234
0.0151
0.0047
=
X (1.6)0.16 x 1
2 x 3Ah = = 0.04266
:. 0.04266 x
0
0.0155
0.0243
0.0256
0.0234
0.0151
0.0047
=
0
0.0006
0.0010
0.0010
0.0010
0.0006
0.0002
0
0.5755
0.9114
0.9741
1.0422
1.116
1.4002
QP =
SRSS Final Results
Presented by Rahul LeslieSeismic Analysis of Multi-storied RC Building
Results
Results
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Set number of modes & Check mass participation
(2.8.4.2, IS:1893(Part 1)-2002) • Consider as many no. of modes so as to have a
total Participating Mass, Σ(Mk) > 90%
• One shouldn’t consider modes having frequencies > 33 Hz
• In case one has considered modes up to 33Hz, but still hasn’t obtained Σ(Mk) > 90%, the only option is a Missing Mass correction
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Set number of Modes & check Mass Participation
ETABS & STAAD• Increase no. of modes
• Check output tables to see – Modes at which participating mass > 90%– Mode having freq. > 33Hz
• Set no. of modes to be considered, accordingly• If all modes are considered up to 33Hz, but still
hasn’t obtained Σ(Mk) > 90%, apply Missing Mass Correction
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
128ETABS: Set no. of modes
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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ETABS: Check mass participation
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ETABS: Check mass participation
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ETABS: Check mass participation
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ETABS: Check mass participation
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ETABS: Check mass participation
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Set this to mode for 33 Hz cut-off freq.
135STAAD: Check mass participation
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136136STAAD: Check mass participation
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
137STAAD: Check mass participation
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
STAAD: Check mass participation
139139STAAD: Check mass participation
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Base Shear Correction
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When dynamic method is followed :• When dynamic analysis is done, a static analysis is
also to be done and base shears compared (7.8.2, IS:1893(Part 1)-2002) – If scale all forces in the ratio as
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Base shear correction• Do analysis with seismic coeff. method
Base shear = Vb(Stat.Anal)
• Do analysis with Resp. Spec. method Base shear = Vb(Dyn.Anal)
• Is Vb(Dyn.Anal) >= Vb(Stat.Anal) ?
If yes (Vb(Dyn.Anal) >= Vb(Stat.Anal)) No problem
If no (Vb(Dyn.Anal) < Vb(Stat.Anal)) scale resp. spec. results by [Vb(Stat.Anal) / Vb(Dyn.Anal)] > 1
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ETABS: Base shear correction
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ETABS: Base shear correction
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ETABS: Base shear correction
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VB(Dyn.Anal) = 1607kNVB(Stat.Anal) = 1769kN
VB(Dyn.Anal) < VB(Stat.Anal)
:.VB(Stat.Anal)/ VB(Dyn.Anal) = 1769/1607 = 1.1 (STAAD)
New Coeff. = Coeff.*1.1 = 0.981*1.1 = 1.08 (ETABS)
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ETABS: Base shear correction
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STAAD: Base shear correction
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Seismic Load Combinations
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ETABS: Load combination
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STAAD: Load combination
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Design Combinations Service Combinations
STAAD: Load combination
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Load Combinations:The analysis results are to be combined using the
following load combinations for RC structures (6.3.1.2, IS:1893(Part 1)-2002, Table 18, IS:456-2000) :
Where EL represents ELx and Ely
#Live load reduction for upper floors as per 3.2, IS:875(Part 2)-1987 not to be included (Note 6, 8.1, IS:875(Part 5)-1987), but reduction as per Table 8, IS:1893 shall be used (7.3.3, IS:1893 (Part 1)-2002)
*To be considered when stability against overturning or stress reversal is critical (foot note to Table 18, IS:456-2000)
Design Combinations:-•COMB-I = 1.5(DL+LL)#
•COMB-II = 1.2(DL+LL±EL)#
•COMB-III = 1.5(DL±EL)•COMB-IV = 0.9DL±1.5EL*
Service Combinations:-•COMB-I = 1.0(DL+LL)•COMB-II = 1.0DL+0.8(LL±EL)•COMB-III = 1.0(DL±EL)
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Load Combinations (cont…):
Design Combinations: Service Combinations:
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
•COMB1 = 1.5(DL+LL)•COMB2 = 1.2(DL+LL+ELx)•COMB3 = 1.2(DL+LL − ELx)•COMB4 = 1.2(DL+LL+ELy)•COMB5 = 1.2(DL+LL − ELy)•COMB6 = 1.5(DL+ELx)•COMB7 = 1.5(DL − ELx)•COMB8 = 1.5(DL+ELy)•COMB9 = 1.5(DL − ELy)•COMB10 = 0.9DL+1.5ELx•COMB11 = 0.9DL − 1.5ELx•COMB13 = 0.9DL+1.5ELy•COMB14 = 0.9DL − 1.5ELy
•COMB1 = 1.0(DL+LL)•COMB2 = 1.0DL+0.8(LL+ELx)#
•COMB3 = 1.0DL+0.8(LL − ELx) #
•COMB4 = 1.0DL+0.8(LL+ELy) #
•COMB5 = 1.0DL+0.8(LL − ELy) #
•COMB6 = 1.0(DL+ELx) #
•COMB7 = 1.0(DL − ELx) #
•COMB8 = 1.0(DL+ELy) #
•COMB9 = 1.0(DL − ELy) #
# Use enhanced SBC for these cases (6.3.5.2 & Table 1, IS:1893(Part 1)-2002)
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Type I :Hard Soil (N > 30)
Type II : Medium Soil(30 ≤ N ≤ 10)
Type III :Soft soil(N < 10)
Pile/Well 50% 25% 25%
Raft 50% 50% 50%
Isolated 50% 25% 0%
Permissible Increase in SBC of soil :-(6.3.5.2 & Table 1, IS:1893(Part 1)-2002)
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Load Combinations (Cont.):The percentage of imposed loads given [0.25 LL ≤ 3 kN/m2, 0.5 LL
> 3kN/m2] shall also be used for ‘whole frame loaded’ condition in the load combinations specified [1.2(DL+LL±EL)] where the gravity loads are combined with the earth quake loads (7.3.3, IS:1893-2002)
Further reduction in imposed load as per 3.2, IS:875 (Part 2)-1987 need not be considered (7.3.3, IS:1893 (Part 1)-2002, similar to Note 6, 8.1, IS:875(Part 5)-1987).
• COMB-I = 1.5[DL+LL]• COMB-II = 1.2[DL+(0.25 LL≤3, 0.5 LL >3)±EL]• COMB-III = 1.5(DL±EL)• COMB-IV = 0.9DL±1.5EL
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Load Combinations (cont…):
For Design:-• COMB1 = 1.5 ( DL + LL )• COMB2 = 1.2 ( DL + 0.25 LL≤3 + 0.5 LL >3 + ELx )• COMB3 = 1.2 ( DL + 0.25 LL≤3 + 0.5 LL >3 − ELx )• COMB4 = 1.2 ( DL + 0.25 LL≤3 + 0.5 LL >3 + ELy )• COMB5 = 1.2 ( DL + 0.25 LL≤3 + 0.5 LL >3 − ELy )• COMB6 = 1.5 ( DL + ELx )• COMB7 = 1.5 ( DL − ELx )• COMB8 = 1.5 ( DL + ELy )• COMB9 = 1.5 ( DL − ELy )• COMB10 = 0.9 DL + 1.5 ELx• COMB11 = 0.9 DL − 1.5 ELx• COMB13 = 0.9 DL + 1.5 ELy• COMB14 = 0.9 DL − 1.5 ELy
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
159
Force Envelopes
160
1.5x(DL + LL)
1.5x(DL + EQx)
1.5x(DL - EQx)
Envelope
161
1.5x(DL + LL)
1.5x(DL + EQx)
1.5x(DL - EQx)
Envelope
162
Torsion & Accidental Eccentricity
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
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Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Accidental eccentricity:• Minimum Design eccentricity edi to be considered
during analysis (7.9.2, IS:1893(Part 1)-2002)
where esi = actual eccentricity bi = breadth of building
-- In case 3D dynamic analysis is carried out, the dynamic amplification factor of 1.5 be replaced by 1.0 (Note 2 to 7.9.2, IS:1893(Part 1)-2002 – Amendment No.1, Jan 2005)
164
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Accidental eccentricity:
165
Specifying Accidental Eccentricity
ETABS• Give eccentricity = 0.05 (ie., 5% of respective dimension) OR (For Seismic Coeff. Method)• For each storey,• If Accidental eccentricity (0.05b) to be provided is in the
same direction as the Actual eccentricity (e), provide Accidental eccentricity as 0.5e+0.05b
• If Accidental eccentricity (0.05b) to be provided is in the opposite direction as the Actual eccentricity (e), provide Accidental eccentricity 0.05b
STAAD• Tick the Accidental Eccentricity / Include Torsion
checkbox
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ETABS: Accidental eccentricity
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ETABS: Accidental eccentricity
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ETABS: Accidental eccentricity
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STAAD: Accidental eccentricity
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Specifying Accidental Eccentricity
STAAD 8i SELECT 4 and above
• If Accidental eccentricity (0.05b) to be given is in the same direction as the Actual eccentricity (e), provide Accidental eccentricity as (0.5e+0.05b)/b
• If Accidental eccentricity (0.05b) to be given is in the opposite direction as the Actual eccentricity (e), provide Accidental eccentricity 0.05
- Note: The above are only to demonstrate ECC and OCC options in STAAD. As per Note 2 to 7.9.2, IS:1893(Part 1)-2002 – Amendment No.1, Jan 2005, only 0.05 need to be given for eccentricity in Response Sectrum Analysis
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STAAD: Accidental eccentricity
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
STAAD.Pro V8i SELECT 4
172
Load Combinations (cont…):
For Design:-• 1.5 ( DL + LL ) 1 Load Case• 1.2 ( DL + LL ± EL x/y ± e ) 8 Load Cases• 1.5 ( DL ± EL x/y ± e ) 8 Load Cases• 0.9 DL ± 1.5 (EL x/y ± e) 8 Load Cases
------------------- 25 Load Cases
For support reactions:-• 1.0 ( DL + LL ) 1 Load Case• 1.0 DL + 0.8 ( LL ± EL x/y ± e ) 8 Load Cases• 1.0 ( DL ± EL x/y ± e ) 8 Load Cases
------------------- 17 Load Cases 42 Load Cases
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Load Combinations (non-ortho beams…):For Design:-• 1.5 ( DL + LL ) 1 Load Case• 1.2 ( DL + LL ± (EL x/y ± e) ± 0.3 (EL y/x ± e))
32 Load Cases• 1.5 ( DL ± (EL x/y ± e) ± 0.3 (EL y/x ± e))
32 Load Cases• 0.9 DL ± 1.5((EL x/y ± e) ± 0.3 (EL y/x ± e))
32 Load Cases-------------------
97 Load Cases
For support reactions:-• 1.0 ( DL + LL ) 1 Load Case• 1.0 DL + 0.8 ((EL x/y ± e) ± 0.3 (EL y/x ± e))
32 Load Cases• 1.0 ( DL ± (EL x/y ± e) ± 0.3 (EL y/x ± e))
32 Load Cases-------------------
65 Load Cases 162 Load Cases
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Reinforced Concrete Design
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Concrete Design
ETABS• Load combinations • Design Code (Indian) • Material: ρ, E, μ, fck, fymain,
fyshear
• Ductile/ordinary• Col. Effective lengths• Etc…
STAAD• Load combinations• Design Code (Indian,
456/13920)• fck, fymain, fyshear
• Load case for beam shear design (DL+LL) (Cl. 6.3.3(b) , IS:13920)
• Col. Effective lengths• Etc…
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Ref:- Fig.4, IS:13920
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ETABS: Concrete Design
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ETABS: Concrete Design
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ETABS: Concrete Design
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ETABS: Concrete Design
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ETABS: Run Analysis
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ETABS: Run Concrete Design
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
183STAAD: Concrete Design
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
184STAAD: Run Analysis
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185
Miscellaneous points
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Selection of method (7.8.1, IS:1893(Part 1)-2002) :• Dynamic analysis to be performed for
1. In case of regular buildings– h > 40 m in Zones IV & V– h > 90 m in Zones II & III
2. In case of irregular buildings– h > 12 m in Zones IV & V– h > 40 m in Zones II & III
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Selection of method (7.8.1, IS:1893(Part 1)-2002) :
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
• When the structure is irregular as per Table 4, IS:1893(Part 1)-2002, the method of dynamic analysis with masses lumped at floor levels, as per 7.8.4.5, IS:1893(Part 1)-2002, cannot be done, rendering computer modelling the only option.
188
Soft Stories (7.10, IS:1893(Part 1)-2002) :• A soft storey is one in which the lateral stiffness is
less than 70 percent of that in the storey above or less than 80 percent of the average lateral stiffness of the three storeys above (4.20, IS:1893(Part 1)-2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
(Fig.4, IS:1893(Part 1)-2002)
189
Soft Stories (7.10, IS:1893(Part 1)-2002) :• In case of buildings with soft stories,
– Dynamic analysis of building be carried out including the strength and stiffness effects of infills, and the members designed accordingly (7.10.2, IS:1893(Part 1)-2002)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
– Alternatively, • Columns and beams of the soft storey be designed for 2.5 times
forces obtained by analysis • Shear walls of the soft storey be designed for 1.5 times forces
obtained by analysis
(7.10.3, IS:1893(Part 1)-2002)
190
Separation Between Adjacent Units (7.11.3, IS:1893(Part 1)-2002) :• To avoid damaging contact when the two units deflect towards
each other
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
• Separation equal to R/2 times the sum of the calculated storey displacements as per 7.11.1, IS:1893(Part 1)-2002 (ie., with
partial load factor of 1.0) of each of them.
• Separation equal to R times the sum of the calculated storey displacements, when floor levels of the adjacent units or buildings are not at the same elevation levels.
191
When to include ductile detailing :-
Ductile detailing provisions shall be adopted in RCC buildings for– More than 5 stories high in zone III– Industrial structure in zone III– Importance factor > 1.0 in zone III– In zone IV & V
(1.1.1, IS:13920-1993)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
Ductile detailing provisions shall be adopted in RCC buildings for– All buildingd in zone III, IV & V
(1.1.1, IS:13920-1993, Edition 1.2)
192
Concluding Remarks
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie
193193
Concluding remarks• The best way to implement advanced seismic analysis
techniques is through an analysis software package.• To use a software package, one has to know it• More importantly, one has to know its limitations,• Still more important, one has to know its pitfalls.• Software Demonstrators/Instructors may tell you the
limitations, but not the pitfalls. Mostly it can be learned only through experience.
• The user should have a good base in Seismic Analysis & Design, and Structural Dynamics. Also a basic understanding of FEM is desirable (but not necessary).
• Also one has to know the code provisions, and have them ready reference (IS:456, SP 34, IS:1893, IS:13920, IS:875 Part-I, II, III)
Seismic Analysis of Multi-storied RC Building Presented by Rahul Leslie